No abstract

Even in case of the Brownian motion as most natural rate of return model it appears too difficult to obtain analytic expressions for most risk measures of constant continuous annuities. In literature the so-called comonotonic approximations have been proposed but these still require the evaluation of integrals. In this paper we show that these integrals can sometimes be computed, and we obtain explicit approximations for some popular risk measures for annuities.Next, we show how these results can be used to obtain fully analytic expressions for lower and upper bounds for the price of a continuously sampled European-style Asian option with fixed exercise price. These analytic lower bound prices are as sharp as those from [Rogers, L.C.G., Shi, Z., 1995. The value of an Asian option. J. Appl. Probab. 32, 1077-1088], if not sharper, but in contrast do not require any longer the evaluation of a two-dimensional or a one-dimensional integral.

In most cases, the transition density function of an Itô stochastic differential equation is not available in closed-form. Using Feynman-Kac integration, we construct an exact recursion scheme for the Laplace transform of the transition density. This allows a very accurate and nearly analytical treatment of a wide range of valuation and econometric problems. Generalizations of our technique to functionals of Lévy processes are also briefly discussed.